Approximate synthesis of weighted l∞-optimal compensators

The problem is to find linear time invariant compensators which minimize an incremental weighted norm of the closed-loop system, and it is equivalent to a minimum distance problem in l₁. The main results establish that, under mild conditions, a minimizer for the problem exists. The author also gives a method for computing an infimizing sequence of suboptimal solutions based on FIR approximation, and a method for computing a converging lower bound on the infimal norm. All required computations are equivalent to finite linear programs